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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 730 · 40 questions
TalentJR

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

NameDateTime takenScore ___ / 40
  1. 1.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 275° (c) 85° (d) 5°
  2. 2.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 5° (c) 10° (d) 95°
  3. 3.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 100° (d) 70°
  4. 4.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 160° (c) 20° (d) 70°
  5. 5.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 80° (d) 50°
  7. 7.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 145° (b) 55° (c) 20° (d) 160°
  8. 8.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 50° (b) 130° (c) 155° (d) 75°
  9. 9.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 115° (b) 140° (c) 155° (d) 65°
  10. 10.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 15° (b) 165° (c) 55° (d) 140°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 40° (d) 130°
  12. 12.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 45° (b) 15° (c) 165° (d) 150°
  13. 13.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 105° (b) 120° (c) 135° (d) 45°
  14. 14.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 115° (c) 65° (d) 25°
  15. 15.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 36° (c) 145° (d) 35°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 120° (c) 150° (d) 30°
  17. 17.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 95° (d) 85°
  18. 18.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 50° (d) 130°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 95° (d) 85°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 59° (c) 60° (d) 61°
  21. 21.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 100° (d) 120°
  22. 22.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 75° (b) 155° (c) 100° (d) 105°
  23. 23.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 150° (c) 125° (d) 55°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 35° (d) 25°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 80° (d) 20°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 135° (d) 45°
  27. 27.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 215° (d) 70°
  28. 28.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 100° (d) 155°
  29. 29.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 155° (b) 90° (c) 115° (d) 270°
  30. 30.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 155° (c) 135° (d) 70°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 60° (d) 30°
  32. 32.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 85° (d) 160°
  33. 33.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 300° (c) 60° (d) 150°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 56° (c) 125° (d) 110°
  35. 35.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 50° (b) 15° (c) 145° (d) 165°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 260° (c) 50° (d) 130°
  37. 37.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 55° (c) 235° (d) 125°
  38. 38.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 200° (c) 20° (d) 21°
  39. 39.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 30° (c) 100° (d) 150°
  40. 40.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 100° (b) 115° (c) 65° (d) 145°

Answer key

  1. 95°
  2. 10°
  3. 110°
  4. 160°
  5. 30°
  6. 50°
  7. 20°
  8. 50°
  9. 115°
  10. 15°
  11. 65°
  12. 15°
  13. 135°
  14. 50°
  15. 35°
  16. 150°
  17. 85°
  18. 80°
  19. 85°
  20. 60°
  21. 80°
  22. 75°
  23. 55°
  24. 25°
  25. 80°
  26. 135°
  27. 145°
  28. 105°
  29. 90°
  30. 135°
  31. 75°
  32. 95°
  33. 60°
  34. 55°
  35. 15°
  36. 130°
  37. 55°
  38. 20°
  39. 30°
  40. 65°

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